Tollin, DJ (18). Computational model of the lateralization of clicks and their echoes, in S. Greenberg and M. Slaney (Eds.), Proceedings of the NATO Advanced Study Institute on Computational Hearing, pp. 77-82 COMPUTATIONAL MODEL OF THE LATERALISATION OF CLICKS AND THEIR ECHOES Daniel J. Tollin Department of Physiology, University of Wisconsin, Madison, WI, 57 and The Sensory Research Unit, Department of Experimental Psychology, University of Oxford, OX1 UD, England. ABSTRACT A computational model was developed to describe the results of psychophysical experiments that investigated the precedence effect with clicks. The model includes several processing steps: First, the signals to the two ears were passed through a bandpass filter simulating the frequency selectivity of the peripheral auditory system. The center frequency of the specific filter was determined by an algorithm that considered both the spectral characteristics of the signals to each ear as well as a "dominance region" around 75 Hz where the interaural delay characteristics of the signals are particularly effective in lateralisation. The filtered signals at each ear were then half-wave rectified and the resultant patterns taken to represent the post-stimulus-time histograms of an auditory nerve fiber's response to a click. The auditory filters were assumed to be linear and time invariant within the small relevant operating range. The simulated temporal response probabilities for each ears signal provided the direct input to a short-term interaural cross-correlation device and a device that extracts information about interaural differences in amplitude. A correlate of the subjective intracranial lateral position was estimated from a linearly weighted sum of the information from the interaural delay and interaural amplitude processors. Lateralisation discrimination "thresholds" were computed in the model by varying the interaural parameters of the stimuli until the lateral position estimate reached a predetermined threshold lateral position. The model was capable of describing many of the major trends in the psychophysical data, even though there was no explicit postonset inhibitory mechanism built into the model. This was a surprising finding since nearly all models of the precedence effect require some type of inhibition. The model provides insights into mechanisms for the precedence effect and binaural hearing in general. 1 INTRODUCTION Echoes are abundant in normal acoustical environments, but our ability to localise sounds in these environments remains remarkably accurate. The precedence effect (PE) refers to the phenomena that arises when two similar sounds arrive in close succession, are perceived as a single auditory event, and are localized largely by directional cues carried in the first-arriving sound [24]. The mechanism that produces the PE is thought to underlie our ability to localise sounds in echoic environments. The neural substrate of the PE is not yet known, but has been recently investigated [25]. One important parameter of echoed sounds is the effect of the delay between a direct sound and its echo on the lateralisability of either the direct or echoed sound. Several studies of the PE using clicks have used the stimulus configurations shown in Figure 1 and a 2- AFC lateralisation discrimination task in which interaural time delay (ITD) jnds were measured for the dichotic click in each Type I Type II Left Right Left Right ITD ICI configuration, and as a function of the interclick-interval (ICI) [] [2] [2]. With these stimuli, the PE can be measured in terms of the lateralisability of the direct sound in comparison to the lateralisability of the echo. An increase in the just-noticeabledifferences (jnds) for interaural delay or interaural level in an echo (Type II) relative to the jnds measured for the direct sound (Type I) is often taken as a measure of the size of the PE. Generally, for ICIs between about 1 and 1 ms, Type I ITD jnds are fairly constant and nearly equal to the jnds for a dichotic click in isolation but the Type II jnds are about 2-8 times larger. The decrease in sensitivity to ITD in echoes is one hallmark of the PE and is considered by the model presented in this paper. Another aspect of directional hearing will also be considered. It is known that observers are particularly sensitive to interaural time and phase differences for frequencies around 75 Hz. Bilsen and Raatgever [1] found a dominance region whereby the frequency components around 7 Hz were more salient in the lateralisation of broadband noise than were neighboring frequencies. Henning [14] used narrowband transients to arrive at the same conclusion. Tollin [22] [2] demonstrated directly a dominance region effect under echoic conditions using broadband clicks in a two-echo configuration. Under certain conditions, Tollin s observers lateralised the two-echo stimuli anomalously - they reported them as arising on the side of the head opposite that expected based on the ITD cue present in the stimulus. Tollin [2] showed that the observers behavior was consistent with their using the IPDs in the frequency band around 75 Hz even though the intensity of that band was less than that of neighboring regions, which contained IPDs indicating the correct lateralisation. The model presented here was designed to explore the hypothesis that the dominance region plays a role in the lateralisation of echoed clicks. ICI ITD time time Figure 1. Stimulus configurations used in discrimination studies of the precedence effect.
2 THE MODEL RED (db) L > R RED (db) L > R IPD (degrees) L < R L < R L > R L < R - - - - - - - - 18 Frequency (Hz) Left Right RED - - - - - - - - - - - - -18 5 1 2 25 Energy Density (db) Energy Density (db) While there have been many models of specific binaural phenomena, no single model has been able to account for a large number of binaural phenomena, particularly the precedence effect [7]. The model developed here was based on the general model of Colburn [][7]. The model was constructed to provide a quantitative account of some aspects of the precedence effect using assumptions that were physiologically reasonable. 2.1 Peripheral frequency selectivity The first step in the model simulates the mechanical tuning properties of the basilar membrane by passing the signals from each ear through a bandpass filter. The second step requires the simulation of the transformation of the mechanical motion of the basilar membrane to the temporal discharge patterns of the auditory nerve fibers. The gamma-tone filter (e.g. [5]) was used to model the filtering properties of the auditory periphery. The impulse response of the specific form of gamma-tone filter used in this model was f n ( n 1) ft h( f, t) = ( ) t e sin( 2πft) 2π where f represents the characteristic frequency (CF) of the filter and n its order. The order of the filter was set equal to 4, a value which Carney and Yin [4] found, using filters of very similar form, provided good descriptions of measured reverse-correlation functions (i.e. estimates of the fiber s impulse response) for a population of low-cf auditory nerve fibers. Figure 2. The right-hand ordinate of the top two panels shows the energy-density spectra of the left and right ear signals for the Type I and Type II stimulus, respectively, both with ICI=8 µs and ITD=2 µs. The left-hand ordinate gives the relative energy density (RED), the ratio of the left and right ear energy densities. The bottom panel shows the interaural phase difference for both stimuli. The spectral characteristics of the sums of the direct and echoed clicks are also considered in the model. As an example, the spectral characteristics for a Type I (top panel) and Type II (middle panel) stimulus with an ICI of 8 µs and an ITD of 2 µs are shown in Figure 2. Notice that the IPD (bottom panel) for both stimuli are identical, but the energy densities of the signals delivered to the left and right ears and the ratio of these energy densities, the Relative Energy Density (RED), are not the same. Tollin [2] showed that Type I ITD jnds with an ICI of 8 µs were nearly equal to the jnd for a dichotic click in isolation, but the Type II jnds for the same ICI were about 5-8 times larger. If the spectral characteristics of these stimuli were important and the interaural cues in the region around 75 Hz were particularly salient, one reason why the Type II stimuli may have been more difficult to lateralise is that the RED cue in that region opposes (i.e. < ) the IPD cue, but in the Type I condition both the RED and IPD signal the same direction (i.e. > ). A kind of time-intensity trade [], then, might be responsible for the reduced sensitivity to ITD in this particular Type II stimulus. This hypothesis will be investigated in the model. The probability that a nerve fiber with a low CF elicits a response is greatest at a particular phase of the input stimulus; in other words, low-cf nerve fibers elicit phase-locked responses (e.g. [1],[1]). Subjecting the simulated responses to a half-wave rectification for positive deflections exceeding 2% of the maximum deflection simulated phase-locking. The resultant provided an estimate of the post-stimulus-time (PST) histogram of the fiber's response to clicks. A further assumption was made that the auditory filters were linear and time-invariant. Thus, the responses to sums of scaled, delayed, and added clicks were equivalent to the sum of the responses to the individual clicks scaled by the same amounts, delayed by the same factors, and added. It was further assumed that the auditory nerve discharge probabilities are generated from this response. 2.2 Cross-correlation mechanism Most models of binaural hearing include as one component a crosscorrelation operation on some aspect of the input signals to the two ears based on Jeffress's [] hypothetical neural network. The temporal response properties of low-frequency auditory nerves are known to be preserved in the anteroventral cochlear nucleus (AVCN) which projects to the MSO []. Physiological studies have implicated the medial superior olive (MSO) as one of the first sites in the ascending auditory system at which there is convergence of neural activity from the two ears ([1],[2]). And there is also physiological and anatomical evidence that the binaural auditory system performs a process not unlike that of cross-correlation ([27]).
The model assumes that the simulated temporal discharge probabilities of the left and right ear auditory nerve responses provided the direct input to a short-term interaural cross-correlation device. This is in agreement with the models of Colburn and his colleagues [8] who assumed that the auditory nerve responses are relayed through the cochlear nuclei to the olivary nuclei (i.e. MSO) with no substantial change in the firing patterns. There is physiological evidence for this assumption as it is known that neurons in the MSO phase-lock to low-frequency sounds [2]. The cross-correlation device essentially compares the timing information from the responses of the fibers in the two ears. The output of the short-term cross-correlation device as a function of time across the interaural delay, τ, for a pair of afferent input fibers with the same characteristic frequency, f, is expressed as +I Τ Rrr ( f, t, τ) = p ( τ) rl ( f, α) rr ( f, α τ) G ( t α) d α LR where the functions r L (f,t) and r R (f,t) represent the temporal response functions of input fibers with characteristic frequency f from the left and right ear, respectively. The parameter Τ represents the total duration of the longest response from which a factor 2*(1/f) was subtracted. Colburn [] specified a weighting function, p(τ), which represents the limited distribution of possible interaural delays. Physiological evidence suggests that there are more binaural neurons in the IC which have their maximum response for small interaural delays than those for large delays [17] and p(τ) can be interpreted to reflect this distribution. The p(τ) used was centered on zero interaural delay and was Gaussian in form with = s [21]. The function G(t-α) was an exponential weighting function which emphasized the most recent inputs to the cross-correlation function. A time constant of 5 ms was chosen because it seemed physiologically reasonable. In the model, the subjective lateral position of a stimulus with only interaural differences in time and no interaural differences in amplitude was specified by the position of the largest peak of the average across the patterns of activity (i.e. across the interaural delay axis, τ) output by the short-term cross-correlator over the duration of the stimulus. 2. Interaural amplitude processor While there is wide acceptance of the use of cross-correlation in models of binaural hearing, there is no widely accepted model of how differences in amplitude are used in conjunction with interaural time differences. One way information about the amplitudes of sounds is encoded in auditory nerve fibers is by increasing their rate of firing with increasing stimulus amplitude (over a limited range) (e.g. [1]). Information about the amplitudes of the stimuli delivered to each ear can be derived from the amplitudes of the simulated discharge probabilities if it is assumed that those probabilities are proportional to the numbers of discharges observed in a given period of time. The summation of the discharges over that time period might be taken as an indication of the relative amplitudes of the stimuli presented to the ears. The interaural amplitude difference in the model, then, was computed as the ratio of the sums of the squares of the simulated neural responses which is given by Ψ( f ) = log where r L (f,t) and r R (f,t) represent the simulated temporal pattern of probable auditory nerve discharges (CF=f) for the left and right ears, respectively. The parameter Τ is the duration of the longest response. 2.4 Lateral position estimator The specific form of the model that relates the lateral position of the auditory image to the ITD and the interaural amplitude difference in the stimulus was a form of the lateral position model as proposed by Hafter [11]. Hafter s model proposed that the perceived intracranial location was dependent upon a weighted linear combination of the interaural differences in time and amplitude. This model has been shown to be successful at predicting certain results of interaural discrimination experiments [7]. In the present model, the lateral position, Ω, in arbitrary units, of the image that results from the stimulation of the nerve fiber with the characteristic frequency f is given by Ω( f ) = { ITD( f ) + α Ψ( f )}/ τ o where the ITD of the maximum peak of the averaged short-term cross-correlation functions, ITD(f), describes the contribution due to the interaural delay. The amplitude function, Ψ(f), was weighted by a trading ratio, α (µs/db), which describes the contribution to the laterality of the stimuli due to interaural differences in amplitude in terms of an equivalent interaural delay. The value for α was set to 2 s/db on the basis of several psychophysical timeintensity trading experiments using low-pass filtered clicks [7]. The normalization factor, τ o, was assumed to be the ITD required for a theoretical observer to reach a threshold level of performance in a 2AFC task with a single click. 2.5 Choosing the center frequency r ( f, t) dt r ( f, t) dt The choice of the CF of the single model auditory nerve fiber depended on the stimulus. Specifically, the CF was chosen based on an analysis of the energy-density spectra of the stimuli delivered to each ear. An algorithm was used to find the local maxima in the energy-density spectrum of the signal presented to either ear closest to 75 Hz. Choosing the CF in this way addresses two ways in which observers might lateralise broadband signals with complex spectral characteristics. First, observers are more sensitive to interaural delay cues in the frequency region near 75 Hz. Second, observers can only use information from spectral regions where there is sufficient energy. Using only a single fiber in the model allows, in effect, a trade between the information from spectral regions with more energy and the information from the dominance region. As an example, consider the Type I and Type II stimulus whose spectral characteristics are shown in Figure 2. The local maxima in the energy density for the Type I stimulus occurs for the left I T 2 L 1 1 T 2 I R
ear s signal at a frequency of 1 Hz. The CF of the model fiber for that particular stimulus would then be set to 1 Hz. A CF=1 Hz would also be used for the Type II example because of the right-ear energy-density maxima. The exact CF depends critically on the ICI and the ITD of the signals because the ripples in the energy density spectra change as these parameters change. This is an important aspect of the model. RESULTS AND DISCUSSION The first data considered are from Experiment 4 of the classic study of Wallach et al. [24]. They used 1-ms clicks presented over headphones in the configuration shown in Figure. The ICI between the onset of the click to the left ear and the onset of the echo click to the right ear was held constant. The ITD of the echo click was varied between -1 µs (left echo click leading) and 1 µs and the observers were asked to indicate whether the image was to the left or right of midline. The top panel shows the psychophysical data. An intriguing aspect of the data is the curious reversal that occurs for large positive ITDs. Based on the stimulus configuration, a lower percentage of left judgments would be expected (i.e < 5%), but the opposite was true. The bottom panel shows the lateral position estimates, Ω, normalised by a τ ο equal to µs to reflect the single-interval task. The CF of the fiber used for these predictions was held constant at Hz because the spectral characteristics of the stimuli are complicated by the 1-ms duration clicks. In addition to the ripples in the spectra due to the time lag between the clicks, there are additional ripples due to the spectrum of the 1- ms click itself. A CF of Hz was a compromise between the locations of the peaks in the energy-densities nearest 75 Hz and the fact that the energy in the band between 75 and 1 Hz was greatly attenuated due to the spectrum of the 1-ms click. The model accurately predicts two noteworthy aspects of the data. First, the reversal for ITDs near µs is predicted. Second, the lack of a significant reversal for large negative ITDs is also predicted. Simple consideration of the energy densities of the stimuli reveals why the reversal occurs. For positive ITDs between and about µs the energy density in the right ear is larger than that in the left in the spectral region around Hz. The IPD, of course, also favours the right ear. More right judgments would be expected. However, by increasing the ITD beyond µs, while the IPD still favours the right ear, the energy density of the stimulus presented to the left ear greatly exceeds that of the right in the region around Hz. Based on the size of the ratio of the left and right ear energy densities in this region, more left judgments would be expected. This is in agreement with the results. No such sign change in the ratio of the energy densities occurs for large negative ITDs (due to the way the stimuli were constructed [24]), so no reversal would be expected. This is also in agreement with the results. Lateral position estimate re: µs 4 2 1-1 L -2 R 2 ms ITD -4-1 -8 - -4-2 2 4 8 1 ITD in 2 nd click (ms) Figure. Top panel shows data from Wallach et al. [24] who used the stimulus shown in the inset of the bottom panel. The bottom panel shows the model predictions in terms of lateral position, Ω re: µs. An alternative explanation of the reversal has been put forward by Hartmann [1]. Hartmann suggested that as the ITD in the echo pair approached 7-8 µs it became comparable to the maximum possible delay that can be experienced in a free-field. He proposed that ITDs larger than those encountered in the freefield would somehow be discounted. This idea forms the basis of the plausibility hypothesis of the PE. While the plausibility hypothesis qualitatively predicts that the lateral judgments might return to midline (i.e. 5% judgments left ) as the ITD exceeds 7-8 µs, it cannot, by itself, predict the reversal. Neither the plausibility hypothesis nor models employing a simple onsetmediated suppression of the binaural information in the echo click [28] can predict the reversal, but the model does. The next data considered are the ITD discrimination data of Tollin [2], who used clicks in the stimulus configurations shown in Figure 1. The threshold lateral position τ o was µs. In the model, the ICI was held constant and lateral position estimates, Ω, were computed over a range of ITDs. The ITDs in the Type I and Type II stimuli were incremented until Ω reached τ o. The ITD at which Ω=τ o was taken as the ITD threshold for a given ICI. These ITD thresholds were then normalised by µs yielding a threshold elevation factor (TEF) [2]. A TEF of 1 indicates that the Type I or Type II stimulus was lateralised as well as a dichotic click in isolation. A TEF of 2 would be expected if the observers lateralised the stimuli based on the IPD
alone. A PE is indicated for Type I TEFs near 1 and Type II TEFs greater than 2.5 for the same ICI [2]. Figure 4 shows the mean TEF as a function of ICI for the Type I and Type II stimuli for two observers in Tollin s study who showed curious but consistent oscillations in their Type II TEFs. The model s predictions are shown as well. The predictions are consistent with several aspects of these data. First, the model accurately predicts larger Type I TEFs than Type II TEFs at ICIs of.1 and.2 ms. This is due to the sign of the RED. Second, predicted Type I TEFs for ICIs between.8 and.4 ms were roughly constant but elevated somewhat from 1. Slightly increased Type I ITD jnds relative to a dichotic click have been observed in other investigations of the PE [] [2]. In that same region of ICIs, predicted Type II TEFs were always larger than the Type I and ranged between around -5. In other words, the model s results are wholly consistent with the precedence effect. This was a surprising result. Recall that there was no artificial post-onset-mediated suppression function built into the model. The decrease in sensitivity to ITD in the echo click relative to the sensitivity to the leading click is an emergent property of the model. And it is also a hallmark of the precedence effect. Again, no inhibitory mechanisms were required. Another interesting aspect of the model was its ability to predict the oscillations in the Type II ITD jnds as reflected by the TEF. Inspection of the spectral characteristics of these stimuli reveals the reason. The directions of the oscillations are consistent with the sign of the RED in the region around 75 Hz. The TEFs are larger when the RED opposes the IPD, but are smaller when the sign of the RED is the same as that of the IPD. Since the predictions are very consistent with the empirical results (up to.4 ms), it is not unreasonable to believe that the observers were using a cue proportional to the RED around 75 Hz.. Notice that for ICIs between.8 and.4 ms the psychophysical Type II TEFs oscillate about a TEF of around 4 but that the Type I TEFs are fairly constant around 1.5, consistent with the precedence effect. The reason for the large Type II TEFs and the only slightly elevated Type I TEFs (in other words, the PE) can be explained as follows. The short-term cross-correlator computes a running estimate of the lateral position due to the ITD in the stimulus. For the Type II stimuli with ICIs greater than about.8 ms, the first few outputs of the running crosscorrelator correspond to a central lateral position due to the diotic click. As time progresses, the response to the echo click begins to be evaluated by the cross-correlator. But the input to the cross-correlator also includes a portion of the response to the first click because of the temporal weighting window G(t). The resultant output at this point is equivalent to the IPD, which for the Type II (and Type I) stimulus is equivalent to an interaural delay of one-half the ITD in the dichotic click (i.e. ITD/2) [2]. These running estimates of the lateral position due to the ITD are then averaged over the time course of the stimulus. What results from this process is simply an averaging of the onset delay and the ongoing delay. How does this simple process translate into increased Type II ITD jnds but not Type I jnds? For the Type II stimulus the onset delay is equal to while the ongoing delay is equal to ITD/2. Threshold Elevation Factor. 5. 4.. 2. 1...8.7 Model Type I Model Type II Type I Type II.1 1. 1. ICI (ms) Figure 4. Tollin s [2] empirical TEFs (filled symbols) and the modeled (open symbols) TEFs for Type I and Type II configurations as a function of ICI. The effective interaural delay, then, is given by the average of these two quantities which is [+ITD/2]/2, or ITD/4. The effective delay for a Type II stimulus is simply one-fourth the ITD in the dichotic echo. If the observers actually used such a cue, then to reach the threshold level of performance, the ITD of the dichotic echo would have to be increased by a factor of 4 greater than the ITD of a dichotic click in isolation. This, of course, would yield a TEF of 4, which is nearly exactly what was observed psychophysically. It appears that the level differences (REDs) in the region around 75 Hz modulate this factor of 4 increase in ITD jnd by a kind of time-intensity trade resulting in ICI-dependent oscillations. Applying the same hypothesis to the Type I configuration results in an effective delay of [ITD+(ITD/2)]/2 which reduces to /4ITD. An ITD in the leading click, then, would need to be a factor of 4/ times the single dichotic click ITD jnd so Type I TEFs of 1. would be expected. It is well documented that the PE is not complete even for Type I-like stimuli and ITD jnds are usually always slightly higher than the ITD jnds for a dichotic stimulus in isolation [][2][2][28]. Most models of the PE assume some type of onset-mediated inhibition or suppression mechanism which affects the directional information in the echoes for a short time after the onset of the initial sound with the inhibition gradually wearing off after about 1 ms [28]. While these models are qualitatively consistent with some aspects of the precedence effect, they cannot account for other aspects, such as anomalous lateralisations [][22][2]. A more computational model of the PE similar to the one in this paper was presented by Blauert and Cobben [2]. It was later extended [18] to include a lateral inhibition mechanism designed to inhibit the outputs of the cross-correlator at adjacent interaural delays for a short time after the onset of the leading stimulus. That model s predictions for echoed narrowband transients were consistent with psychophysical observations using the same stimuli. But, currently there is no physiological evidence of such a lateral inhibition mechanism, and recent data actually contradict such a hypothesis [25].
4 CONCLUSION The novel and surprising aspect of the model presented here was that it predicts the precedence effect with clicks without requiring an explicit onset-mediated suppression or inhibition function required by most models of the PE [18][28]. One serious limitation of the model was that no processes of adaptation, refractoriness, or compressive non-linearities were taken into account. But these processes would surely be expected to contribute even more to a decrease in sensitivity to interaural cues in echoes. This suggests that onset-mediated suppression or inhibition may not necessarily be required for the PE. These are important observations not only for theories on the nature of the PE, lateralisation, and localisation in general, but also because they generate a hypothesis about how neurons selective for interaural timing disparities analyse the temporal response patterns of afferent fibers. It is known that the vast majority of neurons (in the IC at least) are sensitive only to the ongoing delay (or IPD) and not the onset delay [17]. It is proposed here that in response to brief stimuli these binaural neurons simply compute the average of the onset and the ongoing interaural temporal disparities over a short period of about 1ms. 5 ACKNOWLEDGEMENTS Portions of this paper constituted a part of the author s doctoral dissertation submitted to the University of Oxford. Support was generously provided by the NATO Advanced Studies Institute and NIH Grant DC45. Dr. Tom Yin is thanked for his comments on the manuscript. REFERENCES [1] Bilsen, F.A. and Raatgever, J. Spectral dominance in binaural lateralization, Acoustica 28:11-, 17. [2] Blauert, J. and Cobben, W. Some considerations of binaural cross correlation analysis, Acoustica :-14, 178. [] Cant, N.B. and Casseday, J.H. Projections from the anteroventral cochlear nucleus to the lateral and medial superior olivary nuclei, J. 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